The present invention relates to a method of analyzing properties of particles immersed in a body and, in particular, to a method of determining the dimensions of particles immersed in a transparent body and to the corresponding apparatus.
A particular and advantageous application of the present invention consists in the measurement of diameter distribution in particulate material, for example, in powders, vapours, cements, pharmaceutical products, or of particles in transparent colloidal suspensions, for example, in paints, glues, or creams.
The method and the apparatus according to the present invention are based on the following physical principle: each particle struck by an incident electromagnetic field generates a spherical wave, defined as a spherical scattering wave, with an amplitude which varies angularly according to the so-called form factor which is associated with the particle, and is dependent on the size of the particle. Typically, most of the power scattered by a single particle falls within a solid angle the linear aperture of which is of the order of the ratio between the wavelength of the radiation and the size of the particle. At a certain moment, the radiation scattered by all of the particles immersed in a body is the result of the sum of the waves generated by the individual particles. This gives rise to stochastic interference phenomena which generate, on a plane placed at a predetermined distance, an arrangement of small irregular dots or fluctuations in the intensity of the scattered radiation, which are known in the art as speckles.
Conventional techniques for measuring properties of particles which use the principles described briefly above, enable the intensity of the light scattered a long distance from the sample to be measured. This intensity is substantially a mean intensity with respect to the above-mentioned fluctuations upon variation of a detection angle. In a conventional instrument, it is consequently necessary to have sensors which can move between different angular positions, or special multi-element sensors which can simultaneously detect this intensity, averaged over the speckles, in a plurality of angular positions. In any case, a delicate system of optical alignment components is always required for the correct operation of the apparatus. Conventional instruments are consequently somewhat complex and bulky, with quite expensive mechanical and optical parts.
In the document Physical Review Letters, Vol. 85, No. 7, 14 August 2000, two of the authors of which are designated inventors of the present invention, an apparatus is described which comprises a source of a wide laser beam, and a CCD sensor which detects substantially solely the radiation of the laser beam which is scattered by a body subjected to measurement, placed a short distance from the sensor such that the following equations are true:
                    z        <                  dD          λ                                    (        1        )                        and                                                      z        >                              d            2                    λ                                    (        2        )            where λ is the wavelength of the laser beam, z is the distance of the sensor from the body, D is the diameter of the laser beam, and d is a characteristic size of the particles contained in the body, for example, the mean diameter. In this condition, even though the body is illuminated over an area equal to the cross-section of the laser beam, the radiation scattered is propagated in a manner such that each sensitive element of the CCD, or pixel, receives substantially solely radiation scattered by the points of the body in the directions included in a solid angle which has its vertex at the pixel, and which is equal to the solid angle in which the scattered radiation is emitted. A consequence of this phenomenon is that the diameter of the speckles is equal to the diameter of the particles and the value of this diameter does not depend on the distance of the sensor from the body, provided that equations (1) and (2) remain valid.
The instrumental apparatus described in the above-mentioned documents also comprises a lens interposed between the body and the sensor and a metal wire which is extended in the focal plane of the lens, between the lens and the sensor and extending through the focus of the lens. The lens is capable of magnifying the dimensions of the speckles on the sensor so that each speckle covers a plurality of pixels. Moreover, the lens cooperates with the metal wire in a manner such as to focus on the wire the portion of the incident field which is transmitted through the sample, and to deflect the transmitted portion so that it does not reach the sensor.
The CCD sensor simultaneously detects a plurality of values of the intensity of the scattered radiation, one for each of the sensitive elements, and provides corresponding signals to a processing unit. This plurality of values of the intensity of the scattered radiation corresponds to the configuration of speckles detected by the CCD sensor.
An example of the measurement method performed by this apparatus is illustrated in FIG. 1.
In order for processing 100 of these signals to achieve an accurate evaluation of the particle dimensions, it is necessary to perform a series of consecutive instantaneous acquisitions, for example, a number N of acquisitions of the intensity, detected by the CCD sensor, of the radiation scattered by the same body.
As will be appreciated, the processing 100 of the signals comprises, initially, a determination of a plurality of spatial correlation functions of the intensity 110 which correspond to the plurality of scattered radiation intensity values detected in the series of acquisitions. This operation comprises a calculation, for each pixel, of the mean intensity 111 of the intensity values obtained in the series of acquisitions in the same pixel, a calculation of the mean 112 of the mean intensity values obtained in all of the pixels, a calculation of a plurality of spatial correlation functions of the intensity 113, one for each acquisition, and a calculation of a spatial correlation function of the said mean intensity 114. The calculation of the correlation functions may be performed by known methods such as the fast Fourier transform, correcting the result taking into account the finite dimensions of the image. In the drawings, In({right arrow over (x)}) is the scattered radiation intensity value detected in the pixel of coordinate {right arrow over (x)} in the nth acquisition, Ī({right arrow over (x)}) is the mean intensity of the intensity values obtained in the series of acquisitions for each pixel, Ī is the mean of all of the mean intensity values Ī({right arrow over (x)}) with respect to {right arrow over (x)}, Cn(Δ{right arrow over (x)}) is a spatial correlation function of the intensity between two pixels having a vectorial distance Δ{right arrow over (x)} from one another, relating to the nth acquisition, and C0(Δ{right arrow over (x)}) is a spatial correlation function of the mean intensity Ī({right arrow over (x)}).
The processing 100 of the signals then comprises a derivation of an electric-field spatial correlation function 120 from the plurality of intensity spatial correlation functions. This operation comprises a calculation of the mean of the intensity spatial correlation functions 121 relating to the series of acquisitions and a calculation of a correlation function of the electric field 122. The calculation 122 is performed with the use of the so-called Siegert equation which relates the intensity correlation function to the electric-field correlation function. It is consequently possible to calculate the electric-field correlation function in relation to the other quantities previously calculated. In the drawings, C(Δ{right arrow over (x)}) is the mean of the intensity spatial correlation functions and c(Δ{right arrow over (x)}) is the electric-field correlation function.
Finally, the processing 100 of the signals comprises a determination of a power spectrum of the electric field 130 corresponding to the electric-field correlation function. This operation comprises a calculation of a spectrum of the electric-field correlation function 131 by the fast Fourier transform and a calculation of the mean of that spectrum 132 over the values of the transferred wave vector which have the same modulus so as to obtain a power spectrum of the electric field. In the drawings, S({right arrow over (q)}) is the power spectrum of the electric field as a function of the transferred wave vector {right arrow over (q)}, and S(q) is the power spectrum of the electric field as a function of the modulus of the transferred wave vector q.
The electric-field spectrum thus obtained enables the distribution of the dimensions of the particles to be determined by known methods normally used in conventional techniques for the measurement of particle dimensions by measurement of scattered light, which methods will not therefore be described herein.
The method described above may require a large number of acquisitions to be performed in order to be able to eliminate the noise which inevitably afflicts the measurement and thus to obtain an adequate determination of the properties of the particles. Moreover, to be able to calculate the correlation functions of the field on the basis of the intensity correlation functions, it is necessary for the scattered radiation to be capable of being described as a random Gaussian process. Furthermore, although the apparatus is of simple construction, it nevertheless requires correct positioning of the reflecting wire at the focus of the lens.